It sounds like Snickers might have separation anxiety. Many dogs pee and poop from anxiety.
If a dog doesn't want you to leave, it will act out most strongly just after you've left. He is probably pooping within minutes of your departure.
I would try training him out of his separation anxiety first, and then address the potty training. There are a lot of threads here on how to reduce your dog's separation anxiety. Basically, you leave and then come back immediately until he seems okay with that. Then you leave for one minute, then two, then five, then start mixing it up a bit.
Good luck! Let us know if this helps any.
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